VGAM (version 1.0-4)

# lognormal: Lognormal Distribution

## Description

Maximum likelihood estimation of the (univariate) lognormal distribution.

## Usage

lognormal(lmeanlog = "identitylink", lsdlog = "loge", zero = "sdlog")

## Arguments

lmeanlog, lsdlog

Parameter link functions applied to the mean and (positive) $$\sigma$$ (standard deviation) parameter. Both of these are on the log scale. See Links for more choices.

zero

Specifies which linear/additive predictor is modelled as intercept-only. For lognormal(), the values can be from the set {1,2} which correspond to mu, sigma, respectively. See CommonVGAMffArguments for more information.

## Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

## Details

A random variable $$Y$$ has a 2-parameter lognormal distribution if $$\log(Y)$$ is distributed $$N(\mu, \sigma^2)$$. The expected value of $$Y$$, which is $$E(Y) = \exp(\mu + 0.5 \sigma^2)$$ and not $$\mu$$, make up the fitted values. The variance of $$Y$$ is $$Var(Y) = [\exp(\sigma^2) -1] \exp(2\mu + \sigma^2).$$

## References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

rlnorm, uninormal, CommonVGAMffArguments, simulate.vlm.

## Examples

Run this code
# NOT RUN {
ldata2 <- data.frame(x2 = runif(nn <- 1000))
ldata2 <- transform(ldata2, y1 = rlnorm(nn, mean = 1 + 2 * x2, sd = exp(-1)),
y2 = rlnorm(nn, mean = 1, sd = exp(-1 + x2)))
fit1 <- vglm(y1 ~ x2, lognormal(zero = 2), data = ldata2, trace = TRUE)
fit2 <- vglm(y2 ~ x2, lognormal(zero = 1), data = ldata2, trace = TRUE)
coef(fit1, matrix = TRUE)
coef(fit2, matrix = TRUE)
# }


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